452 INDEX Self-adjoint unbounded operator: 15.12 Seminorm: 12.14 Separation (of two sets by a hyperplane): 12.15, prob. 4 Series in a topological vector space: 12.14 Simple convergence, limit: 12.5 Simple normal operator: 15.11 Simplex: 14.3 Spectral radius: 15.2 Spectral value of an element of a normed algebra: 15.2 Spectrum of an element of a Banach algebra: 15.2 Spectrum of a Banach algebra: 15.3 Spectrum of an unbounded operator: 15.12 Square-mtegrable function: 13.11 Stabilizer of a point: 12.10 Stable subspace (for a representation): 15.5 Star algebra: 15.4 Steiner symmetrization: 14.3, prob. 8 Stem's theorem: 14.10, prob. 4 Step function: 13.9 Stieltjes measure: 13.8, prob. 6 Stieltjes' moment problem: 13.20, prob. 5 Stieltjes transform: 14.11, prob. 16 Strict morphism: 12.12 Strong topology: 12.15 Subspace: 12.2 Sum of a series with positive terms: 13.5 Support of a function: 12.6 Support of a measure: 13.19 Symmetric neighborhood: 12.8 Szego-Kolmogoroff-Krein theorem: 15.3, prob.11 Tessellation (G-): 14.1, prob. 6 Thue's theorem: 14.2, prob. 2 Titchmarsh-Kodaira formula: 15.12, prob. 9 Topological group: 12.8 Topological isomorphism of normed (or normable) algebras: 15.1 Topological space: 12.1 Topological zero-divisor: 15.2, prob. 3 Topologically cyclic representation: 15.5 Topologically equivalent families of pseudo- distances: 12.4 Topologically irreducible representation: 15.5 Topologically nilpotent: 15.2, prob. 5 Topologically simple: 15.8 Topology: 12.1 Topology defined by a distance: 12.1 Topology defined by a family of pseudo- distances: 12.4 Topology defined by a family of seminorms: 12.14 Topology of convergence in measure: 13.12, prob. 2 Topology of simple convergence: 12.15 Torus: 14.2 Total mass of a bounded measure: 13.9 Totalizer: 15.5 Trace of an operator: 15.11, prob. 7 Transitively (group acting): 12.10 Translation of a function or measure: 14.1 Transpose of a continuous linear mapping: 12.15 Trivial action: 12.10 Type (p,q) (operator): 13.17, prob. 7 U Unbounded operator: 15.12 Uniformizable space: 12.4 Unimodular group; 14.3 Unitary element: 15.4 Unitary group: 12.15, prob. 8 Universally measurable: 13.9 Upper envelope of a family of real-valued functions: 12.7 Upper integral: 13.5 Upper semicontinuous function: 12.7 Vague topology: 13.4 Vaguely bounded, convergent, continuous: 13.4 von Neumann's ergodic theorem: 12.15, prob.12 von Neumann's theorem on unbounded normal operators: 15.12entiable: